Abstract

Modeling the spatial distribution of base stations (BSs) is essential for evaluating differ-
ent network performance metrics in cellular networks. In this work, we consider the spatial
distribution of actual BSs data from Tier-1 cities of India for one of the leading network
providers. To model this data, we consider the widely used homogeneous Poisson Point
Process (PPP) as a benchmark.
We consider the Thomas and Matern cluster point processes for modeling spatial distribu-
tion of BSs. We have evaluate the performance of these point processes with homogeneous
PPP. Various statistical measures of point process like Repley’s
퐾
-function,
퐿
-function,
Nearest-neighbor hood function, and
퐽
-function are used as Goodness of Fit (GOF) tests
for modeling spatial distribution of BSs. Point-wise envelopes of the statistical measures
are computed for accepting or rejecting the hypothesis at
10%
significance level. The spatial
distribution of BSs in Tier-1 cities exhibit clustering property. However, this clustering is
not characterized completely by either Thomas cluster process or Matern cluster process.
Hence, we further analyze the spatial distribution of BSs using a combination of discrete
and continuous distributions for modeling number of BSs and location of BSs, respectively.
We evaluate the performance of the Poisson distribution with Discrete Exponential, Dis-
crete Weibull, and Zipf-Mandelbrot distributions for modeling the distribution of number
of BSs. Further, we model the spatial location of BSs using Uniform, Gaussian, and Laplace
distributions. We compare the performance of these distributions using GOF tests. The nu-
merical results indicate that the location of BSs can be accurately modeled as a Gaussian
distribution, while, the number of BSs in a given area is best modeled as a Discreet Expo-
nential distribution in the Indian scenario for Tier-1 cities.